Question: A translation of the plane takes $-3 + 2i$ to $-7 - i.$  Find the complex number that the translation takes $-4 + 5i$ to.
Solution: This translation takes $z$ to $z + w,$ where $w$ is a fixed complex number.  Thus,
\[-7 - i = (-3 + 2i) + w.\]Hence, $w = -4 - 3i.$  Then the translation takes $-4 + 5i$ to $(-4 + 5i) + (-4 - 3i) = \boxed{-8 + 2i}.$